Binomial Distribution
Discrete probability of k successes in n independent Bernoulli trials with probability p.
Probability Mass FunctionPMF = P(X = x)
Cumulative Distribution FunctionCDF = F(x)
Probability in an Interval
Compute the probability that X falls between two values. For discrete distributions, this is the sum of probabilities P(X = k) for all integers k from a to b.
P(a ≤ X ≤ b)
Quantiles (Inverse CDF)
Pick a probability p and read the corresponding quantile xₚ where F(xₚ) = p.
Quantile xₚ (where F(xₚ) = p)
In Binomial Distribution, selected probability p: 0.9500 (95.00%)
Parameters
Adjust the parameters and (optionally) add up to 3 curves to compare different settings side‑by‑side.
0 curves shown
Estimating parameters from data
If you’re fitting this distribution to observed data, these are common plug‑in estimates you can start with.
Trials (n)
Count the total number of experiments or trials performed.
Probability (p)
Divide the number of successes by the total number of trials in historical data, or use theoretical probability (e.g., 0.5 for a fair coin).